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Molecular dynamics in polycrystalline testosterone studied by proton NMR
57
Solid State Nuclear Magnetic Resonance, 2 (1993) 57-60 Elsevier Science Publishers B.V., Amsterdam
Molecular dynamics in polycrystalline testosterone studied by proton NMR E.R. Andrew
* and J.M. Radomski ’
of Physics
Departments
and Radiology,
University
of Florida,
Gainesville,
FL 32611,
USA
(Received 8 February 1993; accepted 10 February 1993)
Abstract Polycrystalline testosterone (17/3-hydroxy-4-androsten-3-one, C1sHzs021 has been investigated by proton NMR methods between 70 K and the melting point 428 K. Reductions in dipolar second moment and two well-resolved minima in the spin-lattice relaxation time measured at 25 MHz are ascribed to reorientation of the two methyl groups in the molecule. Activation energies E, characterizing the motions were 6.1+ 0.5 and 11.9* 0.9 kI/mol; the pre-exponential time factors rs were (2.3 +0.1)X lo-l3 and (2.85 f 0.2)~ lo-l3 s, respectively. Keywords:
testosterone; proton NMR; relaxation; molecular dynamics; methyl rotation
Introduction Testosterone (17&hydroxy-4-androsten-3-one, Cr9H2s02) is one of the major biologically active androgenic hormones secreted by the mammalian testis and is responsible for male sex characteristics. It is used clinically for treatment of testicular insufficiency, the suppression of lactation and the therapy of certain kinds of breast cancer. Pure testosterone is a white powder at room temperature. Its melting point is 428 K. The molecular structure is shown in Fig. 1. X-ray studies [l] have shown that the crystal structure is monoclinic, space group P2,, with cell dimensions a = 14.720 A, b = 11.080 A, c = 10.868 A, p = 113.34”. Testosterone is a steroid with the same fused group of four carbon rings as choles-
* Corresponding author. i On leave from Institute of Physics, A. Mickiewicz University, Grunwaldzka 6, 60-780 Poznan, Poland. 0926-2040/93/$06.00
terol, progesterone and cortisone, all recently studied in the solid state by NMR [2-41. Molecular dynamics of both intramolecular and intermolecular motions may be investigated through measurements of NMR proton relaxation in the solid state. In this investigation measurements were made of second moment and T, at 25 MHz from 70 K to the melting point 428 K.
Fig. 1. Molecular structure of testosterone. The carbon skeleton is shown without hydrogen atoms.
0 1993 - Elsevier Science Publishers B.V. All rights reserved
E.R. Andrew,
58
J.M. Radomski
/Solid
State Nucl.
Magn.
Reson.
2 (1993)
57-60
22
TESTOSTERONE Second Moment M2 318 -
1st 14 c 1
1 100
I
I
I
200
300
400
T WI Fig. 2. Temperature dependences of the second moment of polycrystalline testosterone.
Experimental Polycrystalline testosterone was supplied by Sigma Chemical Company, Product No. T-1500, Standard for Chromatography grade. Samples were sealed off in glass ampoules after evacuation at about 373 K for several hours. Measurements of proton spin-lattice relaxation time TI and second moment M2 were made at 25 MHz using a home-built, variable-frequency pulse NMR spectrometer in conjunction with a Varian electromagnet and Nicolet 1180 signal averaging system. A variable-temperature cryostat provided temperatures down to 77 K. Temperatures below 77 K were achieved by pumping the liquid nitrogen bath. The temperature was controlled by a platinum resistance thermometer and Muller bridge to an accuracy and stability of f 1 K. TI was measured by saturation recovery following a train of sixteen 90” pulses. The magnetization was found to recover exponentially within experimental error (- 5%) at all temperatures. Proton second moments were obtained from the initial shape of the free induction decay assuming a Gaussian lineshape [5]. Errors in the determination of TI were estimated to be N 5% and those in M, - 15%.
line narrows in two temperature regions. Below 100 K, M2 falls to a plateau value of 18.2 G2 and in the vicinity of 160 K it falls to a lower plateau value of 17.0 G2. The temperature dependence of the proton spin-lattice relaxation time Tl at 25 MHz is displayed on a logarithmic scale against inverse temperature in Fig. 3. Two well-resolved minima of almost equal depth are observed: Tl = 135 ms at
'.'
Results The temperature dependence of the proton second moment M2 is shown in Fig. 2. The NMR
I
I
I
2
4
I
1
6 6 lOOO/T[K]-'
I
I
10
12
Fig. 3. Temperature dependence of the proton spin-lattice relaxation time TI for polycrystalline testosterone at 25 MHz. The full line is a theoretical curve calculated in the manner described in the text.
E.R. Andrew,
J.M. Radomski
/Solid
State Nucl.
Magn.
Reson.
2 (1993)
155 K (1000/T = 6.5) and T, = 130 ms at 77 K (1000/T = 12.9). Discussion We first consider the second moment. Since the crystal structure is known [l], a theoretical value of second moment may be calculated using the dipolar theory of Van Vleck [6] for a rigid structure: M, = 716.16N-’
zrii6
(1)
where N is the number of protons in the molecular system cocsidered and rij are the interproton distances in A. The X-ray crystal structure gives accurate carbon and oxygen positions. The proton positions were determined from the carhop skeleton assuming C-H distances were 1.09 A and that C-H bonds were tetrahedrally directed. On this basis a rigid lattice second moment of 21.0 G2 was calculated. Rapid reorientation of the methyl groups about their C, axes reduces the second moment and this was calculated [7-111 to be 18.5 G2 for reorientation of one methyl group and 17.0 G2 for reorientation of both methyl groups. We conclude that the rigid value is only reached at lower tempeatures and that the first plateau value in Fig. 2 of 18.2 G* corresponds to reorientation of one methyl group and the second plateau value of 17.0 G* corresponds to reorientation of both methyl groups. This suggests that reorientation of one methyl group is significantly more hindered than the other. This conclusion is confirmed by the relaxation data. The spin-lattice relaxation time T1 measurements shown in Fig. 3 display two minima characteristic of the type first described by Bloembergen et al. [12] and subsequently analyzed in detail by Kubo and Tomita [13]. The full line shown in Fig. 3 has been least-squares fitted by computer to the relaxation expression of Kubo and Tomita [13] extended to more than one independent relaxation process: Tci
T’=Cci i
[
4rci
1+w272, + 1+4w272, 0 CI
Cl CI
59
57-60
We assume two motions, characterized by relaxation constants C, and C, and correlation times T,~ and 7c2, each following an Arrhenius activation law, with activation energy E,, 7,; = Toi exp( Eaj/RT) (3) The agreement of the least-squares fitted calculations with the data in Fig. 3 is excellent. The best agreement was obtained with one motion, generating the high temperature T, minimum, characterized by E, = 11.9 & 0.9 kJ/mol and rol = (2.85 + 0.2) x lo-l3 s and the second motion, generating the low temperature T1 minimum, characterized by E, = 6.1 + 0.5 kJ/mol and T,, = (2.3 -t 0.1) x lo-l3 s. These two motions may be identified with the reorientation of the two methyl groups in the testosterone molecule at positions 18 and 19 (Fig. l), consistent with the second moment data, one group being significantly more hindered than the other. This identification is further confirmed by consideration of the relaxation constants Ci. The reorientation of the methyl groups not only relaxes the methyl protons, but also all the other protons in the molecules in the solid by rapid spin exchange. The relaxation constant C for methyl group reorientation in the presence of rapid spin exchange is given by [14-161: C=---
9 II y4ti* 20N
b6
(4)
where N is the total number of protons in the molecule, IZ is number of protons in the reorienting group and b is the interproton distance. A:suming the commonly accepted value of 1.79 A for the interproton distance b in methyl groups, a value of C is obtained from eqn. (4) which when inserted in eqn. (2) yields a minimum value of T, of 132 ms at 25 MHz, very close to the measured values of 135 ms and 130 ms at the two minima. It is concluded that the only effective relaxation mechanism in solid testosterone in this temperature range arises from reorientation of the two methyl groups in the molecule. In order to decide which methyl group is the more hindered, measurements could be made on a sample of testosterone in which one specific methyl group is replaced by CD,.
1 (2)
60
E.R. Andrew,
Finally, it is of interest to compare the activation energies E, and time factors r0 found for polycrystalline testosterone with those found earlier for polycrystalline progesterone [3]: testosterone 6.1 and 11.9 k.l/mol progesterone 3.4 and 10.9 kI/mol The time factors TV are all in the range (2-3) lo-l3 s.
X
Acknowledgment This work was supported by NIH through grant P41 RR02278.
References 1 P.J. Roberts, R.C. Pettersen, G.M. Sheldrick, N.W. Isaacs and 0. Kennard, J. Chem. Sot. Perkin Trans. 2, (1973) 1978.
J.M. Radomski/Solid
State Nucl.
Magn.
Reson.
2 (1993)
57-60
2 E.R. Andrew and B. Peplinska, Mol. Phys., 70 (1990) 505. 3 E.R. Andrew, K. Jurga, J.M. Radomski and E.C. Reynhardt, Solid State Nucl. Magn. Reson., 1 (1992) 121. 4 E.R. Andrew and M.F. Kempka, Proc. 10th ISM4R Meeting, Morzine Pl-11, 1989. 5 J. Jeneer and P. Brookaert, Phys. Rev., 157 (1967) 232. 6 J.H. Van Vleck, Phys. Rev., 74 (1948) 1168. 7 E.R. Andrew, Nuclear Magnetic Resonance, Cambridge, University Press, Cambridge, 1955. 8 H.S. Gutowsky and G.E. Pake, J. Chern. Phys., 18 (1950) 163. 9 G.W. Smith, J. Chem. Phys., 42 (1965) 4229. 10 G.W. Smith, J. Chem. Phys., 51 (1969) 3569. 11 G. Soda and H. Chihara, J. Phys. Sot. Jpn., 36 (1974) 954. 12 N. Bloembergen, E.M. Purcell and R.V. Pound, Phys. Rev., 73 (1948) 679. 13 R. Kubo and K. Tomita, J. Phys. Sot. Jpn., 9 (1954) 888. 14 E.R. Andrew, W.S. Hinshaw, M.G. Hutchins and R.O.I. Sjoblom, Mol. Phys., 34 (1977) 1965. 15 A. Abragam, The Principles of Nuclear Magnetism, Clarendon Press, Oxford, Chap. 8, 1961. 16 N. Bloembergen, Physica, 15 (1949) 386.
Solid State Nuclear Magnetic Resonance, 2 (1993) 57-60 Elsevier Science Publishers B.V., Amsterdam
Molecular dynamics in polycrystalline testosterone studied by proton NMR E.R. Andrew
* and J.M. Radomski ’
of Physics
Departments
and Radiology,
University
of Florida,
Gainesville,
FL 32611,
USA
(Received 8 February 1993; accepted 10 February 1993)
Abstract Polycrystalline testosterone (17/3-hydroxy-4-androsten-3-one, C1sHzs021 has been investigated by proton NMR methods between 70 K and the melting point 428 K. Reductions in dipolar second moment and two well-resolved minima in the spin-lattice relaxation time measured at 25 MHz are ascribed to reorientation of the two methyl groups in the molecule. Activation energies E, characterizing the motions were 6.1+ 0.5 and 11.9* 0.9 kI/mol; the pre-exponential time factors rs were (2.3 +0.1)X lo-l3 and (2.85 f 0.2)~ lo-l3 s, respectively. Keywords:
testosterone; proton NMR; relaxation; molecular dynamics; methyl rotation
Introduction Testosterone (17&hydroxy-4-androsten-3-one, Cr9H2s02) is one of the major biologically active androgenic hormones secreted by the mammalian testis and is responsible for male sex characteristics. It is used clinically for treatment of testicular insufficiency, the suppression of lactation and the therapy of certain kinds of breast cancer. Pure testosterone is a white powder at room temperature. Its melting point is 428 K. The molecular structure is shown in Fig. 1. X-ray studies [l] have shown that the crystal structure is monoclinic, space group P2,, with cell dimensions a = 14.720 A, b = 11.080 A, c = 10.868 A, p = 113.34”. Testosterone is a steroid with the same fused group of four carbon rings as choles-
* Corresponding author. i On leave from Institute of Physics, A. Mickiewicz University, Grunwaldzka 6, 60-780 Poznan, Poland. 0926-2040/93/$06.00
terol, progesterone and cortisone, all recently studied in the solid state by NMR [2-41. Molecular dynamics of both intramolecular and intermolecular motions may be investigated through measurements of NMR proton relaxation in the solid state. In this investigation measurements were made of second moment and T, at 25 MHz from 70 K to the melting point 428 K.
Fig. 1. Molecular structure of testosterone. The carbon skeleton is shown without hydrogen atoms.
0 1993 - Elsevier Science Publishers B.V. All rights reserved
E.R. Andrew,
58
J.M. Radomski
/Solid
State Nucl.
Magn.
Reson.
2 (1993)
57-60
22
TESTOSTERONE Second Moment M2 318 -
1st 14 c 1
1 100
I
I
I
200
300
400
T WI Fig. 2. Temperature dependences of the second moment of polycrystalline testosterone.
Experimental Polycrystalline testosterone was supplied by Sigma Chemical Company, Product No. T-1500, Standard for Chromatography grade. Samples were sealed off in glass ampoules after evacuation at about 373 K for several hours. Measurements of proton spin-lattice relaxation time TI and second moment M2 were made at 25 MHz using a home-built, variable-frequency pulse NMR spectrometer in conjunction with a Varian electromagnet and Nicolet 1180 signal averaging system. A variable-temperature cryostat provided temperatures down to 77 K. Temperatures below 77 K were achieved by pumping the liquid nitrogen bath. The temperature was controlled by a platinum resistance thermometer and Muller bridge to an accuracy and stability of f 1 K. TI was measured by saturation recovery following a train of sixteen 90” pulses. The magnetization was found to recover exponentially within experimental error (- 5%) at all temperatures. Proton second moments were obtained from the initial shape of the free induction decay assuming a Gaussian lineshape [5]. Errors in the determination of TI were estimated to be N 5% and those in M, - 15%.
line narrows in two temperature regions. Below 100 K, M2 falls to a plateau value of 18.2 G2 and in the vicinity of 160 K it falls to a lower plateau value of 17.0 G2. The temperature dependence of the proton spin-lattice relaxation time Tl at 25 MHz is displayed on a logarithmic scale against inverse temperature in Fig. 3. Two well-resolved minima of almost equal depth are observed: Tl = 135 ms at
'.'
Results The temperature dependence of the proton second moment M2 is shown in Fig. 2. The NMR
I
I
I
2
4
I
1
6 6 lOOO/T[K]-'
I
I
10
12
Fig. 3. Temperature dependence of the proton spin-lattice relaxation time TI for polycrystalline testosterone at 25 MHz. The full line is a theoretical curve calculated in the manner described in the text.
E.R. Andrew,
J.M. Radomski
/Solid
State Nucl.
Magn.
Reson.
2 (1993)
155 K (1000/T = 6.5) and T, = 130 ms at 77 K (1000/T = 12.9). Discussion We first consider the second moment. Since the crystal structure is known [l], a theoretical value of second moment may be calculated using the dipolar theory of Van Vleck [6] for a rigid structure: M, = 716.16N-’
zrii6
(1)
where N is the number of protons in the molecular system cocsidered and rij are the interproton distances in A. The X-ray crystal structure gives accurate carbon and oxygen positions. The proton positions were determined from the carhop skeleton assuming C-H distances were 1.09 A and that C-H bonds were tetrahedrally directed. On this basis a rigid lattice second moment of 21.0 G2 was calculated. Rapid reorientation of the methyl groups about their C, axes reduces the second moment and this was calculated [7-111 to be 18.5 G2 for reorientation of one methyl group and 17.0 G2 for reorientation of both methyl groups. We conclude that the rigid value is only reached at lower tempeatures and that the first plateau value in Fig. 2 of 18.2 G* corresponds to reorientation of one methyl group and the second plateau value of 17.0 G* corresponds to reorientation of both methyl groups. This suggests that reorientation of one methyl group is significantly more hindered than the other. This conclusion is confirmed by the relaxation data. The spin-lattice relaxation time T1 measurements shown in Fig. 3 display two minima characteristic of the type first described by Bloembergen et al. [12] and subsequently analyzed in detail by Kubo and Tomita [13]. The full line shown in Fig. 3 has been least-squares fitted by computer to the relaxation expression of Kubo and Tomita [13] extended to more than one independent relaxation process: Tci
T’=Cci i
[
4rci
1+w272, + 1+4w272, 0 CI
Cl CI
59
57-60
We assume two motions, characterized by relaxation constants C, and C, and correlation times T,~ and 7c2, each following an Arrhenius activation law, with activation energy E,, 7,; = Toi exp( Eaj/RT) (3) The agreement of the least-squares fitted calculations with the data in Fig. 3 is excellent. The best agreement was obtained with one motion, generating the high temperature T, minimum, characterized by E, = 11.9 & 0.9 kJ/mol and rol = (2.85 + 0.2) x lo-l3 s and the second motion, generating the low temperature T1 minimum, characterized by E, = 6.1 + 0.5 kJ/mol and T,, = (2.3 -t 0.1) x lo-l3 s. These two motions may be identified with the reorientation of the two methyl groups in the testosterone molecule at positions 18 and 19 (Fig. l), consistent with the second moment data, one group being significantly more hindered than the other. This identification is further confirmed by consideration of the relaxation constants Ci. The reorientation of the methyl groups not only relaxes the methyl protons, but also all the other protons in the molecules in the solid by rapid spin exchange. The relaxation constant C for methyl group reorientation in the presence of rapid spin exchange is given by [14-161: C=---
9 II y4ti* 20N
b6
(4)
where N is the total number of protons in the molecule, IZ is number of protons in the reorienting group and b is the interproton distance. A:suming the commonly accepted value of 1.79 A for the interproton distance b in methyl groups, a value of C is obtained from eqn. (4) which when inserted in eqn. (2) yields a minimum value of T, of 132 ms at 25 MHz, very close to the measured values of 135 ms and 130 ms at the two minima. It is concluded that the only effective relaxation mechanism in solid testosterone in this temperature range arises from reorientation of the two methyl groups in the molecule. In order to decide which methyl group is the more hindered, measurements could be made on a sample of testosterone in which one specific methyl group is replaced by CD,.
1 (2)
60
E.R. Andrew,
Finally, it is of interest to compare the activation energies E, and time factors r0 found for polycrystalline testosterone with those found earlier for polycrystalline progesterone [3]: testosterone 6.1 and 11.9 k.l/mol progesterone 3.4 and 10.9 kI/mol The time factors TV are all in the range (2-3) lo-l3 s.
X
Acknowledgment This work was supported by NIH through grant P41 RR02278.
References 1 P.J. Roberts, R.C. Pettersen, G.M. Sheldrick, N.W. Isaacs and 0. Kennard, J. Chem. Sot. Perkin Trans. 2, (1973) 1978.
J.M. Radomski/Solid
State Nucl.
Magn.
Reson.
2 (1993)
57-60
2 E.R. Andrew and B. Peplinska, Mol. Phys., 70 (1990) 505. 3 E.R. Andrew, K. Jurga, J.M. Radomski and E.C. Reynhardt, Solid State Nucl. Magn. Reson., 1 (1992) 121. 4 E.R. Andrew and M.F. Kempka, Proc. 10th ISM4R Meeting, Morzine Pl-11, 1989. 5 J. Jeneer and P. Brookaert, Phys. Rev., 157 (1967) 232. 6 J.H. Van Vleck, Phys. Rev., 74 (1948) 1168. 7 E.R. Andrew, Nuclear Magnetic Resonance, Cambridge, University Press, Cambridge, 1955. 8 H.S. Gutowsky and G.E. Pake, J. Chern. Phys., 18 (1950) 163. 9 G.W. Smith, J. Chem. Phys., 42 (1965) 4229. 10 G.W. Smith, J. Chem. Phys., 51 (1969) 3569. 11 G. Soda and H. Chihara, J. Phys. Sot. Jpn., 36 (1974) 954. 12 N. Bloembergen, E.M. Purcell and R.V. Pound, Phys. Rev., 73 (1948) 679. 13 R. Kubo and K. Tomita, J. Phys. Sot. Jpn., 9 (1954) 888. 14 E.R. Andrew, W.S. Hinshaw, M.G. Hutchins and R.O.I. Sjoblom, Mol. Phys., 34 (1977) 1965. 15 A. Abragam, The Principles of Nuclear Magnetism, Clarendon Press, Oxford, Chap. 8, 1961. 16 N. Bloembergen, Physica, 15 (1949) 386.